Sen. Lamar Alexander, R-Tenn., said the Senate Health, Education, Labor and Pensions Committee, which he chairs, will hold hearings starting Sept. 4 “so that Americans will be able to buy affordable health insurance.”

"If your house is on fire, you want to put out the fire, and the fire in this case is the individual health insurance market," Alexander said.

Alexander also said he urged Trump to consider continuing payments temporarily through September to help insurers offer low- or moderate-income families plans with lower copayments and deductibles. Trump has been threatening in tweets to cut the “cost-sharing reduction” payments, worth $7 billion this year, if Congress doesn't pass legislation to repeal and replace Obamacare.

“Without payment of these cost-sharing reductions, Americans will be hurt," Alexander said.

The announcement marks a change in strategy after the failure last week of Republican efforts to repeal and replace Obamacare. Democrats’ calls for a return to “regular order” in the health care debate — with hearings and markups that have been lacking — were echoed by Sen. John McCain, R-Ariz., who returned to the Senate after revealing he has brain cancer. He was one of three Republicans who helped sink the GOP’s last-ditch effort, a “skinny repeal” of limited Obamacare provisions.

Sen. Tim Kaine, a Democrat from Virginia, told USA TODAY that sending health care back to the committees meant lawmakers were answering "the McCain challenge."

"This is a place that really needs to step up its game, and we can do it, there’s no reason we can’t," said Kaine, a member of the HELP Committee.

But Rep. Mark Meadows, R-N.C., who heads the hard-line conservative Freedom Caucus, sounded doubtful over whether the Senate could find a bipartisan solution on health care. Meadows, a close ally of Trump's, is pushing senators to continue to look for ways to repeal Obamacare.

“I guess Lamar is not up for re-election,” he said.

Alexander said that the goal is for lawmakers on the committee to agree on a "small, bipartisan and balanced” fix for the individual market by mid-September so that insurance companies can set their premiums for 2018.

The committee will hear from state insurance commissioners, patients, governors, health care experts and insurance companies. Senators who aren't on the HELP panel would still have a chance to participate in the process.

“I think it’s really clear that the path to improving health care … has to be through working across the aisle," said Sen. Patty Murray, of Washington, the HELP Committee's ranking Democrat.

Senate Majority Leader Mitch McConnell of Kentucky has said it’s time to move on from efforts to repeal and replace Obamacare because he doesn’t have the votes. But other senators on committees with health care jurisdiction may keep the issue alive.

“We can’t move on from health care because Obamacare is a mess," GOP Sen. Ron Johnson of Wisconsin told CNN on Tuesday. As chairman of the Homeland Security and Governmental Affairs panel, he said he can hold oversight hearings to "lay out the realities" on health care.

Alexander also said that he would be in touch with Sens. Orrin Hatch, R-Utah, and Ron Wyden, D-Ore., the chairman and ranking member of the Finance Committee, which has jurisdiction over Medicaid.

Wyden told USA TODAY on Tuesday that the Finance panel will first take up the Children’s Health Insurance Program, which requires legislative action to extend funding beyond Sept. 30, 2017.

"That’s an opportunity to help kids and also work on fixes to the Affordable Care Act," Wyden said.

But it's unclear whether Hatch wants to spend more time on Obamacare. He noted that he already knows the impact of the law, which is why so many have called for its repeal.

"As we work through these challenges, one thing is certain: There should be no Obamacare bailouts without significant reforms,” he said.

Trump has urged Republicans to not give up on a repeal while threatening to cut insurance subsidies, calling them “bailouts.” White House adviser Kellyanne Conway said Sunday that Trump would make a decision this week on whether to cut the payments, which 7 million people qualified for this year.

If a new HealthCare Bill is not approved quickly, BAILOUTS for Insurance Companies and BAILOUTS for Members of Congress will end very soon!

Senate Minority Leader Chuck Schumer of New York noted that insurers in three states — North Carolina, Pennsylvania and Idaho — have issued two sets of proposed rates for 2018: one rate if the administration makes cost-sharing payments and another if they do not. In all three states, he said the proposed rates absent payments are 20% higher.

"The ball is in the President’s court: he can make the payments as the law requires and needs, or he can sabotage our healthcare system and impose a Trump Premium Tax of 20% higher premiums on the American people next year by not extending the cost-sharing program," Schumer said.

Senate Minority Whip Dick Durbin of Illinois told USA TODAY that Trump would pay the political price if his decision affects premiums and the availability of insurance.

"He naively believes that his fingerprints aren’t at the scene of this crime," Durbin said. "The American people are going to think the health care system cratered on your watch, Mr. President, and you could have helped and you failed to do it."

Some Republicans acknowledge the need to continue the payments, at least in the short term, to stabilize the marketplace.

“That’s his decision,” Sen. Bob Corker, R-Tenn., told reporters Monday. “Regardless of what is being said, I think he understands the effect it has on low-income citizens, and likely will continue those payments.”

Hatch said he doesn’t know whether Trump should make the payments. Asked whether people potentially would be harmed if Trump doesn’t, Hatch said, “I think so, but I don’t blame the president either."

"He’s not getting much cooperation from Congress, and frankly I can see why he’s fed up and taking that position," Hatch said.